2024

最新文章

• Aperiodic chain recurrence classes of C1-generic diffeomorphisms AI翻译
  作者：Bonatti, Christian; Shinohara, Katsutoshi
  作者单位：Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Hitotsubashi University
  摘要：We consider the space of C-1-diffeomorphims of a three dimensional closed manifold equipped with the C-1-topology. It is known that there are open sets in which C-1-generic diffeomorphisms display uncountably many chain recurrence classes, while only countably many of them may contain periodic orbits. The classes without periodic orbits, called aperiodic classes, are the main subject of this paper. The aim of the paper is to show that aperiodic classes of C-1-generic diffeomorphisms can exhibi...
• Stability of the Faber-Krahn inequality for the short-time Fourier transform AI翻译
  作者：Gomez, Jaime; Guerra, Andre; Ramos, Joao P. G.; Tilli, Paolo
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; ETH Zurich; Polytechnic University of Turin
  摘要：We prove a sharp quantitative version of the Faber-Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit delta(f;omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta (f;\Omega )$\end{document} which measures by how much the STFT of a function f is an element of L2(R)\d...
• Scalar curvature rigidity of convex polytopes AI翻译
  作者：Brendle, Simon
  作者单位：Columbia University
  摘要：We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.
• Morse inequalities for ordered eigenvalues of generic self-adjoint families AI翻译
  作者：Berkolaiko, Gregory; Zelenko, Igor
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：In many applied problems one seeks to identify and count the critical points of a particular eigenvalue of a smooth parametric family of self-adjoint matrices, with the parameter space often being known and simple, such as a torus. Among particular settings where such a question arises are the Floquet-Bloch decomposition of periodic Schr & ouml;dinger operators, topology of potential energy surfaces in quantum chemistry, spectral optimization problems such as minimal spectral partitions of man...
• N-point spherical functions and asymptotic boundary KZB equations (vol 229, pg 1, 2022) AI翻译
  作者：Stokman, J. V.; Reshetikhin, N.
  作者单位：University of Amsterdam; Tsinghua University; University of California System; University of California Berkeley
• Persistence of heterodimensional cycles AI翻译
  作者：Li, Dongchen; Turaev, Dmitry
  作者单位：Imperial College London
  摘要：A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least C 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C<^>{2}$\end{document} , we...
• Long range order for three-dimensional random field Ising model throughout the entire low temperature regime AI翻译
  作者：Ding, Jian; Liu, Yu; Xia, Aoteng
  作者单位：Peking University
  摘要：For d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d\geq 3$\end{document}, we study the Ising model on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...
• Purity and 2-Calabi-Yau categories AI翻译
  作者：Davison, Ben
  摘要：For various 2-Calabi-Yau categories C for which the classical stack of objects M has a good moduli space p: M. M, we establish purity of the mixed Hodge module complex p!Q M. We do this by using formality in 2CY categories, along with etale neighbourhood theorems for stacks, to prove that the morphism p is modelled etale-locally by the semisimplification morphism from the stack of modules of a preprojective algebra. Via the integrality theorem in cohomological Donaldson-Thomas theory we then p...
• The largest prime factor of n2+1and improvements on subexponential ABC AI翻译
  作者：Pasten, Hector
  作者单位：Pontificia Universidad Catolica de Chile
  摘要：We combine transcendental methods and the modular approaches to the ABC conjecture to show that the largest prime factor of n(2)+1isatleastofsize(log(2)n)(2)/log(3)nwhere log k is the k-th iterate of the logarithm. This gives a substantial improvement on the best available estimates, which are essentially of size log2ngoing back to work of Chowla in 1934. Using the same ideas, we also obtain significant progress on sub expoential bounds for the ABC conjecture, which in a case gives the first i...
• The Onsager conjecture in 2D: a Newton-Nash iteration AI翻译
  作者：Giri, Vikram; Radu, Razvan-Octavian
  作者单位：Princeton University
  摘要：For any gamma<1/3, we construct a nontrivial weak solution to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies u is an element of C gamma(R(t)xT(x)(2)) . In particular, the constructed solution does not conserve energy and, thus, settles the flexible part of the Onsager conjecture in two dimensions. The proof involves combining the Nash iteration technique with a new linear Newton iteration.